Which expression represents the sum of n and 7 multiplied by 3? *
1. n + 7 x 3
2. (n + 7) x 3
3. (n + 7) ÷ 3
4. (n - 7) x 3

The probability that the 12-sided solid gets 3 , 9 or 11 is P ( A ) = 1/4 and the expected number of times is n = 45

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that the the 12-sided solid gets 3 , 9 or 11 be P ( A )

Now , the value of P ( A ) is

Let the number of outcomes when rolling a 12-sided solid = 12

The number of times the solid is rolled = 180 times

So , the total number of outcomes = 12 x 180 = 2160

And , the probability of getting a 3 = 1/12

The probability of getting a 9 = 1/12

The probability of getting a 11 = 1/12

So , the total probability of getting a 3 , 9 or 11 = 3/12 = 1/4

The total expected number of times = 45

Hence , the probability is 1/6

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The $28.50 amount Jamie and Dana has to spend and the items that they bought expressed as an equation indicates;

An equation is a mathematical statement that indicates equivalence between two expression.

The amount Jamie and Dana takes to the concert = $28.50

The cost of hot dogs = $1.25

Cost of soft pretzels = $2.50

Cost of a water bottle = 50 cents
Let x represent the number of hot dogs and let y represent the number of soft pretzels Jamie and Dana bought together

The cost of the two water bottles they buy (one each) = 2 × 50 cents = $1

The equation that determines the number of hot dogs and soft pretzels they buy is therefore; 1.25·x + 2.50·y + 1 = 28.50

The graph of the equation can be found by making y the subject of the formula as follows;

1.25·x + 2.50·y = 27.50

2.50·y = 28.50 - 1 - 1.25·x

y = (27.50 - 1.25·x) ÷ 2.50 = 11 - 0.5·x

y = 11 - 0.5·x

The above equation is a linear function

The points on the graph are;

(0, 11), (2, 10), (4, 9), (6, 8), (8, 7), (10, 6), (12, 5), (14, 4), (16, 3), (18, 2), (20, 1), (22, 0)

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Answer:

38.25, 39 if you need to round up

Step-by-step explanation:

8 fluid ounces for each customer times 153 customer = 1224 ounces, divide that by 32 to equal your quarts

The center of mass for the system (x, y) is \(\left(\frac{a m+b M}{m+M}, 0\right)\).

What is center of mass?

The unique location where the weighted relative position of the scattered mass adds to zero is known as the center of mass in physics. Here is where a force may be applied to produce a linear acceleration without also producing an angular acceleration.

The center of mass is a position defined relative to an object or system of objects. It is the average position of all the parts of the system, weighted according to their masses.

Centre of mass is

\(x=\frac{m a+M b}{m+M}\)

and y=0

\((x, y)=\left(\frac{a m+b M}{m+M}, 0\right)\)

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Kimberly had 2 times as many marshmallows as Chris. After eating 15 each, Kimberly had 3 times as many marshmallows as Chris. Kimberly had 60 marshmallows at first.

Generally, Let's call the number of marshmallows that Kimberly had at first X.

We know that Kimberly had 2 times as many marshmallows as Chris at first, so Chris had X/2 marshmallows.

After eating 15 each, Kimberly had X - 15 marshmallows, and Chris had X/2 - 15 marshmallows.

We also know that Kimberly had 3 times as many marshmallows as Chris after eating 15 each, so

(X - 15) = 3 * (X/2 - 15).

(X - 15) - 3 * (X/2 - 15) = 0

Then, we can simplify the left side of the equation:

X - 15 - 3 * X/2 + 45 = 0

Combining like terms, we get:

-3 * X/2 + X - 15 + 45 = 0

Simplifying further:

-X/2 =-30

X = 60

Therefore, Kimberly had 60 marshmallows at first.

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Using the coordinates of the vertices of a polygon (-3, 1), (-3, 3), (-1, 5), (2, 4), and (2, 1) the perimeter of the polygon is 16.0 units

The perimeter is calculated by summing the sides

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

(-3, 1) and (-3, 3) =√{(-3 - -3)² + (3 - 1)²} = 2

(-3, 3) and (-1, 5) = √{(-1 - -3)² + (5 - 3)²} = 2√2

(-1, 5) and (2, 4) = √{(2 - -1)² + (4 - 5)²} = √10

(2, 4) and (2, 1) = √{(2 - 2)² + (1 - 4)²} = 3

(2, 1) and (-3, 1) = √{(-3 - 2)² + (1 - 1)²} = 5

The perimeter = 2 + 2√2 + √10 + 3 + 5

The perimeter = 15.9907

The perimeter = 16.0 units

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Answer:

  (T, C, J) = (in dollars)

     (10000, 10000, 0),

     (15000, 4915.97, 84.03),

     (18181.82, 1680.67, 137.51)

Step-by-step explanation:

There are a number of ways to approach this question. We have chosen an approach that determines the investments required to achieve interest rate targets.

__

For an overall interest rate of I, the proportion that must be invested at rate I1 < I < I2 is ...

  proportion at I1 = (I2 -I)/(I2 -I1)

Similarly, the proportion that must be invested at I2 is what's left over. It can be computed similarly:

  proportion at I2 = (I -I1)/(I2 -I1)

__

We want an overall interest rate of $2000/$20000 = 10%.

Given available interest rates of 9%, 11%, and 130%, we need to have investments at a rate lower than 10% and at a rate higher than 10%.

If we use only the options for 9% and 11% (no junk bonds), then we can compute ...

  proportion at 9% = (11 -10)/(11 -9) = 1/2

  proportion at 11% = (10 -9)/(11 -9) = 1/2

1st Option:

  $10,000 in treasury bills; $10,000 in corporate bonds

__

Suppose we want to achieve a 13% return on our investments at 11% and 130%. Then the proportion invested at 9% will use this value for I2:

  proportion at 9% = (13 -10)/(13 -9) = 3/4

Of the remaining 1/4 of the money, we can achieve a 13% return by mixing the investments like this:

  proportion at 11% = (130 -13)/(130 -11) = 117/119

  proportion at 130% = (13 -11)/(130 -11) = 2/119

2nd option:

  $20,000 × 3/4 = $15,000 in treasury bills

  $5000 × 117/119 = $4,915.97 in corporate bonds

  The remaining amount, $84.03 in junk bonds

__

Let's suppose we want a 20% return on our investment in junk bonds and corporate bonds. Then the proportion of the money invested at 9% will be ...

  proportion at 9% = (20 -10)/(20 -9) = 10/11

And the proportion at 11% will be ...

  proportion at 11% = (130 -20)/(130 -11) = 110/119 . . . (of the remaining 1/11 of the funds)

3rd option:

  $20,000 × 10/11 = $18,181.82 in treasury bills

  $1,818.18 × 110/119 = $1,680.67 in corporate bonds

  The remaining amount, $137.51 in junk bonds

_____

Additional comment

The most that could be invested in Junk Bonds is $165.29. If the remainder is invested in Treasury Bills, then the overall return will be $2000. (You could consider this to be a 4th option.)

We can write k(x) as the composition of g(x) and f(x).

k(x) = g(f(x))

A composition of two functions means that we need to evaluate one function in the other one.

Here we have the functions:

f(x)=  x²

g(x) = √(x - 1)

h(x) = 2x + 3

And we know that:

k(x) = √(x² - 1)

So we have a square root, then we need to evaluate g(x), and the argument is a square, then we need to evaluate in f(x), the composition is:

k(x) = g(f(x))

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Since there are 4 sick students with flu for each sick student with other illness, then, there are 4 students with flu for each 5 sick students.

Multiply the ratio 4:5, which is the proportion of students with flu to sick students, by the total amount of sick students, to find how many students had the flu:

Therefore, 48 students had the flu.

Answer: 88.5

Step-by-step explanation:

Step 1: Address the formula, input parameters & values.

Input parameters & values:

The given numbers are 82 & 95

Step 2: Find the sum of the given two numbers.

sum = 82 + 95 = 177

Step 3: Divide the sum by 2 to get the average.

average = 177/2

= 88.5

On solving the provided question, we can say that Therefore, you would need multiply  approximately 27.84 pounds of food each day for your horse.

One of the four mathematical operations, along with arithmetic, subtraction, and division, is multiplication. Mathematically, adding subgroups of identical size repeatedly is referred to as multiplication. The multiplication formula is multiplicand multiplier yields product. To be more precise, multiplicand: Initial number (factor). Number two as a divider (factor). The outcome is known as the result after dividing the multiplicand as well as the multiplier. Adding numbers involves making several additions. as in 5 x 4 Equals 5 x 5 x 5 x 5 = 20. 5 times by 4 is what I did. This is why the process of multiplying is sometimes called "doubling."

First, we need to convert the weight of the horse from kilograms to pounds, so:

678 kg x 2.20462 lbs/kg = 1495.69 lbs

Next, we need to calculate how many Mcal the horse needs per day:

0.0333 Mcal/kg x 678 kg = 22.58 Mcal/day

Then, we can convert the Mcal to kcal:

22.58 Mcal/day x 1000 kcal/Mcal = 22,580 kcal/day

Finally, we can divide the total daily kcal needed by the kcal per pound of food to find the total pounds of food needed:

22,580 kcal/day ÷ 810 kcal/lb = 27.84 lbs/day

Therefore, you would need approximately 27.84 pounds of food each day for your horse.

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Both figures r similar (given )

\( \frac{5}{2.5} = \frac{3}{1.5} = \frac{2}{1} = \frac{4}{x} \\ \frac{2}{1} = \frac{4}{x} \\ \frac{ \cancel{2}}{1} = \frac{ \cancel{4}^ { \tiny{2}}}{x} \\ x = 2 \: \: ans\)

9514 1404 393

Answer:

  C.  -10

Step-by-step explanation:

Whole numbers are non-negative integers. -10 is not a whole number.

Answer:

See below

Step-by-step explanation:

Here we need to prove that ,

\(\sf\longrightarrow sin^2\theta + cos^2\theta = 1 \)

Imagine a right angled triangle with one of its acute angle as \(\theta\) .

\(\sf\longrightarrow sin\theta =\dfrac{p}{h} \\\)

\(\sf\longrightarrow cos\theta =\dfrac{b}{h} \)

And by Pythagoras theorem ,

\(\sf\longrightarrow h^2 = p^2+b^2 \dots (i) \)

Where the symbols have their usual meaning.

Now , taking LHS ,

\(\sf\longrightarrow sin^2\theta +cos^2\theta \)

\(\sf\longrightarrow \bigg(\dfrac{p}{h}\bigg)^2+\bigg(\dfrac{b}{h}\bigg)^2\\\)

\(\sf\longrightarrow \dfrac{p^2}{h^2}+\dfrac{b^2}{h^2}\\ \)

\(\sf\longrightarrow \dfrac{p^2+b^2}{h^2} \)

\(\sf\longrightarrow\cancel{ \dfrac{h^2}{h^2}}\\ \)

\(\sf\longrightarrow \bf 1 = RHS \)

Since LHS = RHS ,

Hence Proved !

I hope this helps.

Answer:

x = 4

Step-by-step explanation:

if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.

DE is such a line , then

\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\)  ( substitute values )

\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )

3x = 2(x + 2)

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

Solution is 10. How?

I dont know if it helps but tell me if it does

Answer:

width : 21ft

length : 63ft

Step-by-step explanation:

(42ft + w) + (42ft + w) + w + w = 168ft

42ft + w + 42ft + w + w + w = 168ft

w + w + w + w = 168ft - 42ft - 42ft

4w = 84ft

w = 84ft ÷ 4

w = 21ft

so,

width : 21ft

length : 21ft + 42ft = 63ft

Answer:

m<BAC= 110 degrees

Step-by-step explanation:

Since the outside angle m<BCD is 130 degrees the inside angle m<BCA would be 50 degrees. At this point you should know that inside angles of a triangle add up to 180 degrees so add the two angles that you know then subtract from 180 degrees. 50+20= 70 degrees and 180-70= 110 degrees.

Answer:

B) 19 years old

Step-by-step explanation:

x+y=30

2y-3=x

--------------

2y-3+y=30

3y-3=30

3y=30+3

3y=33

y=33/3

y=11

x+11=30

x=30-11

x=19

Answer:

Remi (but barely)

Step-by-step explanation:

6 minutes & 30 seconds is 370 seconds total.

Divide that by 2, now you have 185 seconds per lap.

9 minutes & 6 seconds is 546 seconds total.

Divide that by 3, now you have 182 seconds per lap.

Remi's average lap time is 3 seconds faster than Jack's.

Hope this helped. :)

Answer:

210.5.

Step-by-step explanation:

To simplify the expression 30.5•7-3+2 and ensure that the order of operations is clear, we can place parentheses around the first two terms:

(30.5•7) - 3 + 2

Now, we can perform the multiplication first:

213.5 - 3 + 2

Then, we can simplify by performing the addition and subtraction:

210.5

Therefore, with the added parentheses, the expression simplifies to 210.5.

As understand you need to get 30 by placing parenthesis in the expression:

There are two ways I can think of.

1) The 5*7 is 35 so we can subtract 5 to get 30:

2) Another way is 5*6 = 30 and it is achieved as:

Answer:

The elevation of the airplane decreases by 9 km.

Step-by-step explanation:

We use the distance-rate-time formula: d = rt.

Here, the rate is r = 0.15 km/min and the time is t = 60 min. Simply plug these into the formula:

d = rt

d = 0.15 * 60 = 9 km

So, the change in elevation in the last 60 minutes is 9 km. However, note that the rate is negative (-0.15 km/min), which means that the elevation actually is decreasing.

Thus, the answer is: the elevation of the airplane decreases by 9 km.

~ an aesthetics lover

Answer:

The elevation of the airplane _decrease_ by __9____ km

Step-by-step explanation:

Take the rate and multiply by the time to get the distance traveled

-.15 km per minute * 60 minutes

- 9 km

The plane will go down 9 km in that 60 minutes

Answer: 87

Step-by-step explanation:

3,132/9 = 348

348x1.5 = 522

522-435 = 87

i think?

Answer:

the answer would be:

\(2n^3\)

Hope that helps! :)

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

hope it helps :)

Answer:

w = 120

x = 60

y = 120

z = 60

Step-by-step explanation:

w = 120 (vertically opposite angles)

sum of co interior angles is 180

⇒ w + x = 180 and x + y = 180

w + x = 180

⇒ 120 + x = 180

⇒ x = 180 - 120

⇒  x = 60

x + y = 180

⇒  60 + y = 180

⇒   y = 180 - 60

⇒   y = 120

z = x (corresponding angles)

z = 60

If the recycling center gives Marry $0.40 per pound money she will earn for both days of recycling is $11.20

What information is given in the question?

Marry collected 16.2 pounds of cans for the recycling center on Monday.

On Tuesday, she collected 11.8 pounds.

The recycling center gives her $0.40 per pound.

According to the given question:

To find how much money she will earn for both days of recycling, calculate money earned on Monday and Tuesday. Then add the amount to get the amount earned on both days.

Money earned by Marry on Monday = 16.2 x 0.40 = $6.48

Similarly, money earned by Marry on Tuesday = 11.8 x 0.40 = $4.72

Therefore, Total money earned by Marry for both days

= 6.48 + 4.72

= $11.20

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Using the system of equation and determinant given, the value of k is any real number except -1/3

The determinant is a scalar value that can be computed from the elements of a square matrix. It is a useful tool in linear algebra and is used in many applications, including solving systems of linear equations, finding the inverse of a matrix, and calculating the volume of a parallelepiped.

Given the system of equations 3x + y + 2 = 0, -4x + 2y = k and 3x - y - 3k = 0.

We can write these equations in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix and B is the constant matrix.

A = [3 1 2]

[-4 2 k]

[3 -1 -3k]

X = [x]

[y]

[k]

B = [0]

[0]

[0]

To find the value of k for which the system is consistent, we need to find the determinant of the coefficient matrix.

|A| = (3)(2k) - (1)(-4) + (2)(3) = 6k + 2

For the system of equations to be consistent, the determinant of the coefficient matrix should not be equal to zero.

So, |A| = 6k + 2 ≠ 0

Therefore, the value of k can be any real number except -1/3.

So, the value of k can be any real number except -1/3. The system of equations is consistent for all real numbers except -1/3.

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As a result, option two (3.50) is correct.

Step-by-step explanation:                                                    
                                   
The code chunk that allows you to filter the data frame for chocolate bars with at least 70% cocoa and a rating of at least 3.5 pounds is as follows

∴ filter(Cocoa, percent>='70%'&Rating>=3.5)


Therefore, the code you write is facet wrap(Cocoa. Percent). Facet wrap() is a function in this code chunk that allows you to wrap a variable's facets. All of the ingredients are derived from cocoa beans. Cacao solids (the "brown" part, which contains health benefits and the unmistakable chocolatey flavor) and cacao butter (the "white" part, which contains the chocolate's fatty component) are split in proportion.


As a result, 3.5 appears in row 1 of your Tibble.

Other options I (iii), and (iv) are incorrect because the question states that any rating greater than or equal to 3.5 points can be considered a
high rating, and the rating here should be 3.5, not 3.75, 4.25, or 4

So, option (ii) is correct.  


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